Anisotropic elastic properties of triclinic 2D materials using density functional theory with application to rhenium disulfide

In this paper, we present a rigorous and systematic approach for evaluating the linearized elastic stiffnesses of triclinic 2D materials. Unlike orthorhombic and hexagonal materials, triclinic 2D materials exhibit in-plane extension-shear coupling effects wherein axial stresses can cause a shear strain and a shear stress can induce axial strains. In the presented approach, the elastic stiffnesses of a 2D material are evaluated by curve fitting a constitutive model to either the strain energy densities or the stresses obtained for different strain states in strain space. The approach can be used to determine all the mechanical properties of a triclinic 2D material, including the coefficients of mutual influence that characterize the extension-shear coupling. The proposed approach is illustrated by evaluating the stiffness tensor of triclinic 2D rhenium disulfide using first principles calculations. The Young’s and shear moduli, the Poisson’s ratios and the coefficients of mutual influence of rhenium disulfide are presented along with the directional dependence of its mechanical properties. In addition, the degree of anisotropy of rhenium disulfide is discussed.